document.write( "Question 1163487: How long is the shadow cast on the ground (represented by the xy-plane) by a pole that is eight meters tall, given that the sun’s rays are parallel to the vector [5, 3, −2]? \n" ); document.write( "

Algebra.Com's Answer #787583 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "How long is the shadow cast on the ground (represented by the xy-plane) by a pole that is eight meters tall,
\n" ); document.write( "given that the sun’s rays are parallel to the vector [5, 3, −2]?
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document.write( "First, the projection of the given 3D-vector to the (x,y)-plane is the vector V = [5,3].\r\n" );
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document.write( "It defines the direction to the sun in this plane, and its length is  | V | =  =  = .\r\n" );
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document.write( "Next, if the angle of sun rays with the Earth surface (which we interpret as the plane (x,y)) is ,  then\r\n" );
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document.write( "     = .\r\n" );
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document.write( "From the other side, if L is the shadow length, then\r\n" );
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document.write( "     = ,\r\n" );
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document.write( "which implies for the shadow length\r\n" );
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document.write( "     L =  =  =  = 23.32 meters (rounded).    ANSWER\r\n" );
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